Brentano’s Kalam argument

I’ve been unimpressed by attempts to defend the Kalam, but I was deeply impressed by Brentano’s defense of it.

Thesis: if any activity or process is measured by time, it must have a beginning. 

N.B. When we speak of a thing measured by time, we include not only parts of larger processes and activities, but even the sum or totality of them.

1.) If some process lacks a beginning, it cannot be at any determinate part of its process at a given time. The consequent is absurd, therefore, etc.

Take the simplest case of an object moving inertially in a straight line. The factors that determine where it is are its velocity, the amount of time it has been moving, and where it started moving. Assume that the third factor is removed. Then we are left with nothing that determines why the object is in one place rather than another. All there is to the motion is how fast it moved for how long, neither of which can account for it being in any determinate place.

2.) Assume that some object has been moving for an infinite time at speed V and has reached location N. Therefore, if it moved at .5V it would have reached .5N. Call this .5N point M. But then the distance to M (.5N) is equal to the distance from M to N (.5n) thus, a finite line is equal to one which has no beginning, that is, a line having two endpoints stretches to a line with no endpoint; or a finite object is the same length as an infinite one, all of which are impossible.

Objection: Brentano can only account for a process of unlimited continuity. What if the process was the infinite repetition of some finite sequence? Why would it be impossible to have a universe where an object was created, moved ten feet, and was annihilated, and this repeated ad infinitum?

Response: The same can be reached starting with the number of times the process has happened. Let the number of repetitions be N, and the turnover duration be doubled getting us M repetitions. We then get an M that is equal to .5N.

These observations were made many times after Brentano. The basic rules of algebra do not allow for the infinite to enter into equations as a quantity. If we start with ∞+1=∞, then, if we subtract like quantities we get 1=0.

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18 Comments

  1. July 24, 2014 at 6:38 pm

    I’ve always liked Brentano’s argument on this point, too.

  2. July 27, 2014 at 5:51 pm

    Kalam rests on the premise that the universe had a beginning in time, yet—as St. Thomas shows in, e.g., De Æternitate Mundi—this can only be known by faith (cf. also this).

  3. July 27, 2014 at 7:08 pm

    Re: “any activity or process is measured by time”:
    If “any activity is measured by time”, that means it changes/moves, because time is the measure of change.
    The statement “any process is measured by time” is tautological, since a process is something undergoing change, and time is the measure of that change.
    So, the argument is simply: “If there is a changing activity or a process, it must have a beginning [in time].” The universe changes. Ergo, the universe had a beginning [in time].

    Distinguo: Something in the universe having a beginning in time is different than the universe itself having a beginning in time, since time is ultimately measured with respect to the whole universe. It’s not like time existed first (@, say, -∞ < t < 1 sec), then later in time the universe existed (@, say, t = 1 sec). Time makes no sense without reference to a changing being. Time and the universe come into existence together.

    • July 27, 2014 at 10:43 pm

      But you’re re-writing the thesis to be a claim about things in time, as well as overlooking the note right after the thesis that was written explicitly to say that we’re speaking not just about parts of the temporal series but the whole as well.

      The time reference is most important in the second proof where it becomes a same quantity evaluated according to changes in other variables. This, again, applies both to the parts of a motion and the sum or whole of them.

      • July 28, 2014 at 4:22 pm

        Can you explain more: “When we speak of a thing measured by time, we include not only parts of larger processes and activities, but even the sum or totality of them.”?
        Time is a measurement. A measurement is a relation of two things. How can there be a time for “the sum or totality of them” (i.e. a universal, absolute time for the universe)? With what is that time measured against? Itself? How can the measurer and the measured be the same?

        Also, regarding point (1), why must we be able to determine “why the object is in one place rather than another” with insufficient information?
        And point (2): There seems to be a confusion between two types of infinity: (1) infinity in the sense of undetermined and (2) a real infinity. Of course saying an undetermined object is finite (or is anything else) is absurd; that’s to confuse potentiality and actuality. If he’s speaking of a real infinite line, then he has to show that such a line is possible and can really exist.

      • July 29, 2014 at 8:19 am

        With what is that time measured against? Itself? How can the measurer and the measured be the same?

        A whole can be measured by one of its parts: this is what we do when we say the universe is about 13 billion years old. Even more of an identification would be possible: if Pharaoh’s forearm determines one cubit, then not only can we measure Pharaoh himself by this, but even his own forearm – his tailor might be interested in knowing where to cut the cuffs.

        why must we be able to determine “why the object is in one place rather than another” with insufficient information?

        because it is a datum of experience. An investigation into some blue thing, as such, would try to explain why it was blue; one into a thing at a given place, assuch, needs to explain why it’s at a given place.

        There seems to be a confusion between two types of infinity: (1) infinity in the sense of undetermined and (2) a real infinity.

        Brentano only needs infinity as a putative duration of the universe in time.

        If he’s speaking of a real infinite line, then he has to show that such a line is possible and can really exist.

        But Brentano is denying the possible existence of precisely such things! (at least if they’re moving)

  4. Negationes etiam non summe amamus said,

    July 28, 2014 at 8:18 pm

    What are your thoughts on Bonaventure’s “Kalam”?

  5. socraticum said,

    July 31, 2014 at 11:27 am

    I’d be inclined to deny the premise that, in the case of an infinite universe, therer is a “totality of time”: it seems to me that such a totality implies that the whole is bounded (in some respect) which is precisely what infinity in that respect denies.

    • July 31, 2014 at 1:18 pm

      so you’d say that if, over an infinite time, an object moved at .5V would get to exactly the same place as if it moved at V? Not that it would go just as far, mind you, but that it would get to the same place?

      • socraticum said,

        August 1, 2014 at 2:49 am

        No, what I’m saying is that that absurdity posed in the scenario presupposes a first place they both left from, which is what infinity denies.

        If they haven’t moved from the same place at different speeds, then there is no way to determine where each one is unless one has prior info of each objects location and speed. (i.e. the precise position of both objects in infinite motion is not determinable a priori)

      • August 1, 2014 at 8:34 am

        If they haven’t moved from the same place at different speeds, then there is no way to determine where each one is unless one has prior info of each objects location and speed.

        Right, but that’s the problem. We end up committed to a description of motion that cannot, even in principle, explain why a moving object is at a determinate point at a determinate time, that is, we end up having to defend the idea that there is absolutely no reason at all why a thing is at one point rather than another, in spite of this being perhaps the very first thing we know about natural things. Very few things are more manifest from sensation.

        We still disagree over what the scenario presupposes. I say it only assumes the axiom that over the same time, velocities travel distances proportional to their speeds. The infinite enters into Brentano’s argument only as this “same time” between two different hypothetical velocities.

      • socraticum said,

        August 2, 2014 at 1:49 pm

        We end up committed to a description of motion that cannot, even in principle, explain why a moving object is at a determinate point at a determinate time, that is, we end up having to defend the idea that there is absolutely no reason at all why a thing is at one point rather than another . . .

        Perhaps I’m being dense, but isn’t it the case that this is to be expected? I’ve always thought that the nature of spatial extension is such that there is no formal difference between point A and point B. (The kind of specification that occurs through something like Aristotle’s natural place or a coordinate system seems to be extrinsic to the extension of space itself). As such, it would seem to be impossible to give a reason why a motion ends up or passes through a given point.

        I say it only assumes the axiom that over the same time, velocities travel distances proportional to their speeds.

        But that axiom leaves the situation undetermined, doesn’t it? If two objects are lined up now which have always been (and will always be) moving at different velocities, wouldn’t we just say that, at any given time in the past or the future, they would not be lined up? Perhaps I’m not seeing the proposed absurdity: I took it to be that things travelling at different speeds cover the same space in equal times.

      • socraticum said,

        August 2, 2014 at 1:56 pm

        I just realized I was misreading the argument. I still think, however, there is a hidden fallacy here:

        Assume that some object has been moving for an infinite time at speed V and has reached location N. Therefore, if it moved at .5V it would have reached .5N. Call this .5N point M. But then the distance to M (.5N) is equal to the distance from M to N (.5n)

        Namely, at first when one says “has reached location N”, one is merely talking about a point reached. Then, when one says “if it moved at .5V, it would have reached .5N” one switches to using N to represent a distance: but, for “.5N” to have any meaning, N must be the kind of distance which is divisible into two equal parts: but the parts of a distance are equal when the endpoints of those distances are able to coincide. Since, however, the distance “N” is infinite in one direction, it does not have an endpoint in that direction. Consequently, whenever that distance is divided, it is divided into two parts, one of which cannot (in principle) be equal to the other.

  6. Michael said,

    August 2, 2014 at 8:55 pm

    Can you give a citation for where Brentano makes this argument? I’d deeply appreciate it. Thank you!

    • August 7, 2014 at 8:46 am

      In English it’s Brentano’s On The Existence of God: Lectures given at the Universities of Wurzburg and Vienna trans. Susan Krantz (1987) paragraph 410 pp. 281-2.


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